[[1]}] Let \(\Gamma _1\)  and \(\Gamma _2\)  be two threshold graphs and let \(\pi _1(\Gamma _1)\)  and \(\pi _{2}(\Gamma _2)\)  be degree sequences of \(\Gamma _1\)  and \(\Gamma _2\)  respectively. If \(\pi _1(\Gamma _1) = \pi _{2}(\Gamma _2)\) , then \(\Gamma _1 \cong \Gamma _2\) .

The Laplacian spectrum of threshold graphs \(\Gamma \) , which we denote by \(\ell -spec(\Gamma )\) , have been studied in [2]}, [3]}. In [2]}, the formulas for the Laplacian spectrum, the Laplacian polynomial, and the number of spanning trees of a threshold graph are given. It is shown that the degree sequence of a threshold graph and the sequence of eigenvalues of its Laplacian matrix are almost the same and on this basis, formulas are given to express the Laplacian polynomial and the number of spanning trees of a threshold graph in terms of its degree sequence.
